Twyman went from being an awkward player, cut three straight times by his high-school basketball team, to being a star for the University of Cincinnati, where he averaged 24.6 points and 16.5 rebounds per game as a senior, earning All-America honours. He played professionally with the Royals, who moved from Rochester, New York, to Cincinnati, following the 1956–57 season. Twyman scored 15,840 points (an average of 19.2 points per game) and registered 5,424 rebounds in an 11-year (1955–66) career. Considered one of the best pure-shooting forwards in the NBA, he was inducted into the Naismith Memorial Basketball Hall of Fame in 1983.

The compassion that Twyman, who was of Irish descent, showed for the stricken Stokes, an African American, at a time when segregation was still commonplace in the United States set an example that resonated far beyond the boundaries of sports. The relationship between the two men began with a shared hometown, Greater Pittsburgh. When both were drafted by the Royals out of college in 1955, they drove to Rochester together to begin their professional careers. In the final game of the 1957–58 season, Stokes, already recognized as one of the NBA’s dominant forwards, fell hard and struck his head. Later he lapsed into a coma. Diagnosed with posttraumatic encephalopathy, Stokes was virtually immobile and bedridden for the remaining 12 years of his life. (He died of a massive heart attack at age 36 in 1970 and was inducted into the Hall of Fame in 2004.) When Stokes’s family could not pay his medical bills, Twyman pursued workmen’s compensation benefits for Stokes and had himself appointed his friend’s legal guardian. Twyman spent countless hours caring for Stokes and taught him to communicate by blinking his eyes, with resultant publicity touching off a wave of worldwide goodwill.

From 1958 Twyman also organized an annual charity event (originally a basketball tournament played for Stokes’s benefit) that provided help to former professional players in need. “If people want to remember me for helping Maurice and not what I did on the basketball court, that’s fine,” Twyman said after he retired. He later worked as an analyst on NBA telecasts, and from 1972 to 1996 he served as chairman and chief executive of Super Food Services. The story of Twyman and Stokes’s relationship was told in the motion pictureMaurie (1973). In 2013 the NBA created the Twyman-Stokes Teammate of the Year Award, which was to be given annually to the league’s “ideal teammate.”